Deghosting benefits traditional seismic processing and is a prerequisite to all inverse-scattering-series based processing. The freedom of choosing a convenient reference medium (and associated Green’s function) means Green’s theorem offers a flexible framework for deriving useful algorithms including deghosting. Among advantages over traditional deghosting methods are: (1) no need for Fourier transforms over receivers and sources, and (2) can accommodate a horizontal or non-horizontal measurement surface, the latter of particular interest for ocean bottom and onshore applications. The theory of Green’s theorem-derived deghosting is presented, and its first application on deep-water Gulf of Mexico synthetic (SEAM) and field data is reported. The source and receiver deghosting algorithms work with positive and encouraging results.